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Summary points
The bias introduced by random measurement error will be different depending on whether the error is in an exposure variable (risk factor) or outcome variable (disease)
Random measurement error in an exposure variable will bias the estimates of regression slope coefficients towards the null
Random measurement error in an outcome variable will instead increase the standard error of the estimates and widen the corresponding confidence intervals, making results less likely to be statistically significant
Increasing sample size will help minimise the impact of measurement error in an outcome variable but will only make estimates more precisely wrong when the error is in an exposure variable
Introduction
Random measurement error is a pervasive problem in medical research and clinical practice. 1 It occurs when measurements fluctuate unpredictably around their true values and is caused by imprecise measurement tools or true biological variability, or both. For instance, when blood pressure is assessed with a sphygmomanometer, random error may arise from imprecise measurement due to rounding error or from true diurnal or day to day variation in pressure. 2 3 Hence, a blood pressure reading obtained at a single occasion may differ by an unpredictable (random) amount from an individual's usual blood pressure. 3
Random measurement error differs from systematic measurement error. 4 Systematic error occurs when the measurement error, after multiple measurements, does not average out to zero. The measurements are consistently wrong in a particular direction-for example, they tend to be higher than the true values. In the case of blood pressure measurement, systematic error may be due to improper calibration of the sphygmomanometer or improper arm cuff size, and averaging multiple blood pressure measurements will not help estimate true blood pressure.
While the impact of systematic error is generally well appreciated by researchers and addressed in epidemiological and clinical studies, the impact of random measurement error is often less well appreciated. Since the total error in a variable with random measurement error averages out to zero, many people assume that the effects of random measurement error on the estimate of the association between an exposure (risk factor) and an outcome (disease) obtained from a regression model will also cancel out (that is, have no effect on the estimate). Others have observed that random...